Bad Topology got after applying modifier
Your topology looks decent.
I'm pretty sure your array modifier didn't match start and end 100%. That created an overlap which you see in your 1. screenshot. Repairing this is tedious, it would be much simpler to go back to before you applied the array and fixing it in the base shape. If you use a segment of a circle or a sphere and then rebuild the circle/sphere from the modified segment with a circular array, make sure not to touch the outermost vertices, as they have to align perfectly in the end.